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Simplifying (v + 12)(2v + -6) = 0 Reorder the terms: (12 + v)(2v + -6) = 0 Reorder the terms: (12 + v)(-6 + 2v) = 0 Multiply (12 + v) * (-6 + 2v) (12(-6 + 2v) + v(-6 + 2v)) = 0 ((-6 * 12 + 2v * 12) + v(-6 + 2v)) = 0 ((-72 + 24v) + v(-6 + 2v)) = 0 (-72 + 24v + (-6 * v + 2v * v)) = 0 (-72 + 24v + (-6v + 2v2)) = 0 Combine like terms: 24v + -6v = 18v (-72 + 18v + 2v2) = 0 Solving -72 + 18v + 2v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 9v + v2) = 0 Factor a trinomial. 2((-12 + -1v)(3 + -1v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -1v)' equal to zero and attempt to solve: Simplifying -12 + -1v = 0 Solving -12 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1v = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1v = 0 + 12 -1v = 0 + 12 Combine like terms: 0 + 12 = 12 -1v = 12 Divide each side by '-1'. v = -12 Simplifying v = -12Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Solution
v = {-12, 3}
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